EigenValuesAdvection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: EigenValuesAdvection.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description:
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iostream>
 
#include <ADRSolver/EquationSystems/EigenValuesAdvection.h>
 
using namespace std;
 
namespace Nektar
{
string EigenValuesAdvection::className =
    GetEquationSystemFactory().RegisterCreatorFunction(
        "EigenValuesAdvection", EigenValuesAdvection::create,
        "Eigenvalues of the weak advection operator.");
 
EigenValuesAdvection::EigenValuesAdvection(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : EquationSystem(pSession, pGraph)
{
}
 
void EigenValuesAdvection::v_InitObject(bool DeclareFields)
{
    EquationSystem::v_InitObject(DeclareFields);
 
    // Define Velocity fields
    m_velocity = Array<OneD, Array<OneD, NekDouble>>(m_spacedim);
    std::vector<std::string> vel;
    vel.push_back("Vx");
    vel.push_back("Vy");
    vel.push_back("Vz");
    vel.resize(m_spacedim);
 
    GetFunction("AdvectionVelocity")->Evaluate(vel, m_velocity);
 
    // Type of advection class to be used
    switch (m_projectionType)
    {
        // Discontinuous field
        case MultiRegions::eDiscontinuous:
        {
            // Define the normal velocity fields
            if (m_fields[0]->GetTrace())
            {
                m_traceVn = Array<OneD, NekDouble>(GetTraceNpoints());
            }
 
            string advName;
            string riemName;
            m_session->LoadSolverInfo("AdvectionType", advName, "WeakDG");
            m_advObject = SolverUtils::GetAdvectionFactory().CreateInstance(
                advName, advName);
            m_advObject->SetFluxVector(&EigenValuesAdvection::GetFluxVector,
                                       this);
            m_session->LoadSolverInfo("UpwindType", riemName, "Upwind");
            m_riemannSolver =
                SolverUtils::GetRiemannSolverFactory().CreateInstance(
                    riemName, m_session);
            m_riemannSolver->SetScalar(
                "Vn", &EigenValuesAdvection::GetNormalVelocity, this);
 
            m_advObject->SetRiemannSolver(m_riemannSolver);
            m_advObject->InitObject(m_session, m_fields);
            break;
        }
        // Continuous field
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
            string advName;
            m_session->LoadSolverInfo("AdvectionType", advName,
                                      "NonConservative");
            m_advObject = SolverUtils::GetAdvectionFactory().CreateInstance(
                advName, advName);
            m_advObject->SetFluxVector(&EigenValuesAdvection::GetFluxVector,
                                       this);
            break;
        }
        default:
        {
            ASSERTL0(false, "Unsupported projection type.");
            break;
        }
    }
}
 
/**
 * @brief Get the normal velocity
 */
Array<OneD, NekDouble> &EigenValuesAdvection::GetNormalVelocity()
{
    // Number of trace (interface) points
    int nTracePts = GetTraceNpoints();
 
    // Auxiliary variable to compute the normal velocity
    Array<OneD, NekDouble> tmp(nTracePts);
 
    // Reset the normal velocity
    Vmath::Zero(nTracePts, m_traceVn, 1);
 
    for (int i = 0; i < m_velocity.size(); ++i)
    {
        m_fields[0]->ExtractTracePhys(m_velocity[i], tmp);
 
        Vmath::Vvtvp(nTracePts, m_traceNormals[i], 1, tmp, 1, m_traceVn, 1,
                     m_traceVn, 1);
    }
 
    return m_traceVn;
}
 
void EigenValuesAdvection::v_DoInitialise()
{
}
 
EigenValuesAdvection::~EigenValuesAdvection()
{
}
 
void EigenValuesAdvection::v_DoSolve()
{
    int nvariables = 1;
    int dofs       = GetNcoeffs();
    // bool UseContCoeffs = false;
 
    Array<OneD, Array<OneD, NekDouble>> inarray(nvariables);
    Array<OneD, Array<OneD, NekDouble>> tmp(nvariables);
    Array<OneD, Array<OneD, NekDouble>> outarray(nvariables);
    Array<OneD, Array<OneD, NekDouble>> WeakAdv(nvariables);
 
    int npoints = GetNpoints();
    int ncoeffs = GetNcoeffs();
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            dofs = ncoeffs;
            break;
        }
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
            // dofs = GetContNcoeffs();
            // UseContCoeffs = true;
            break;
        }
    }
 
    cout << endl;
    cout << "Num Phys Points = " << npoints << endl; // phisical points
    cout << "Num Coeffs      = " << ncoeffs << endl; //
    cout << "Num Cont Coeffs = " << dofs << endl;
 
    inarray[0]  = Array<OneD, NekDouble>(npoints, 0.0);
    outarray[0] = Array<OneD, NekDouble>(npoints, 0.0);
    tmp[0]      = Array<OneD, NekDouble>(npoints, 0.0);
 
    WeakAdv[0] = Array<OneD, NekDouble>(ncoeffs, 0.0);
    Array<OneD, NekDouble> MATRIX(npoints * npoints, 0.0);
 
    for (int j = 0; j < npoints; j++)
    {
 
        inarray[0][j] = 1.0;
 
        /// Feeding the weak Advection oprator with  a vector (inarray)
        /// Looping on inarray and changing the position of the only non-zero
        /// entry we simulate the multiplication by the identity matrix. The
        /// results stored in outarray is one of the columns of the weak
        /// advection oprators which are then stored in MATRIX for the futher
        /// eigenvalues calculation.
        m_advObject->Advect(nvariables, m_fields, m_velocity, inarray, outarray,
                            0.0);
        Vmath::Neg(npoints, outarray[0], 1);
        switch (m_projectionType)
        {
            case MultiRegions::eDiscontinuous:
            {
                break;
            }
            case MultiRegions::eGalerkin:
            case MultiRegions::eMixed_CG_Discontinuous:
            {
                for (int i = 0; i < nvariables; ++i)
                {
                    // m_fields[i]->MultiplyByInvMassMatrix(WeakAdv[i],WeakAdv[i]);
                    // Projection
                    m_fields[i]->FwdTrans(outarray[i], WeakAdv[i]);
 
                    m_fields[i]->BwdTrans(WeakAdv[i], outarray[i]);
                }
                break;
            }
        }
 
        /// The result is stored in outarray (is the j-th columns of the weak
        /// advection operator). We now store it in MATRIX(j)
        Vmath::Vcopy(npoints, &(outarray[0][0]), 1, &(MATRIX[j]), npoints);
 
        /// Set the j-th entry of inarray back to zero
        inarray[0][j] = 0.0;
    }
 
    ////////////////////////////////////////////////////////////////////////////////
    /// Calulating the eigenvalues of the weak advection operator stored in
    /// (MATRIX) using Lapack routines
 
    char jobvl = 'N';
    char jobvr = 'N';
    int info = 0, lwork = 3 * npoints;
    NekDouble dum;
 
    Array<OneD, NekDouble> EIG_R(npoints);
    Array<OneD, NekDouble> EIG_I(npoints);
 
    Array<OneD, NekDouble> work(lwork);
 
    Lapack::Dgeev(jobvl, jobvr, npoints, MATRIX.get(), npoints, EIG_R.get(),
                  EIG_I.get(), &dum, 1, &dum, 1, &work[0], lwork, info);
 
    ////////////////////////////////////////////////////////
    // Print Matrix
    FILE *mFile;
 
    mFile = fopen("WeakAdvMatrix.txt", "w");
    for (int j = 0; j < npoints; j++)
    {
        for (int k = 0; k < npoints; k++)
        {
            fprintf(mFile, "%e ", MATRIX[j * npoints + k]);
        }
        fprintf(mFile, "\n");
    }
    fclose(mFile);
 
    ////////////////////////////////////////////////////////
    // Output of the EigenValues
    FILE *pFile;
 
    pFile = fopen("Eigenvalues.txt", "w");
    for (int j = 0; j < npoints; j++)
    {
        fprintf(pFile, "%e %e\n", EIG_R[j], EIG_I[j]);
    }
    fclose(pFile);
 
    cout << "\nEigenvalues : " << endl;
    for (int j = 0; j < npoints; j++)
    {
        cout << EIG_R[j] << "\t" << EIG_I[j] << endl;
    }
    cout << endl;
}
 
void EigenValuesAdvection::GetFluxVector(
    const Array<OneD, Array<OneD, NekDouble>> &physfield,
    Array<OneD, Array<OneD, Array<OneD, NekDouble>>> &flux)
{
    ASSERTL1(flux[0].size() == m_velocity.size(),
             "Dimension of flux array and velocity array do not match");
 
    int nq = physfield[0].size();
 
    for (int i = 0; i < flux.size(); ++i)
    {
        for (int j = 0; j < flux[0].size(); ++j)
        {
            Vmath::Vmul(nq, physfield[i], 1, m_velocity[j], 1, flux[i][j], 1);
        }
    }
}
} // namespace Nektar